The maximal numerical range $W_0(A)$ of a matrix $A$ is the (regular) numerical range $W(B)$ of its compression $B$ onto the eigenspace $\mathcal L$ of $A^*A$ corresponding to its maximal eigenvalue. So, always $W_0(A)\subseteq W(A)$. Conditions under which $W_0(A)$ has a non-empty intersection with the boundary of $W(A)$ are established, in particular, when $W_0(A)=W(A)$. The set $W_0(A)$ is also described explicitly for matrices unitarily similar to direct sums of $2$-by-$2$ blocks, and some insight into the behavior of $W_0(A)$ is provided when $\mathcal L$ has codimension one.

This note proves the following inequality: If $n=3k$ for some positive integer $k$, then for any $n$ positive definite matrices $\bA_1,\bA_2,\dots,\bA_n$, the following inequality holds: \begin{equation*}\label{eq:main} \frac{1}{n^3} \, \Big\|\sum_{j_1,j_2,j_3=1}^{n}\bA_{j_1}\bA_{j_2}\bA_{j_3}\Big\| \,\geq\, \frac{(n-3)!}{n!} \, \Big\|\sum_{\substack{j_1,j_2,j_3=1,\\\text{$j_1$, $j_2$, $j_3$ all distinct}}}^{n}\bA_{j_1}\bA_{j_2}\bA_{j_3}\Big\|, \end{equation*} where $\|\cdot\|$ represents the operator norm. This inequality is a special case of a recent conjecture proposed by Recht and R\'{e} (2012).

For the class of matrices over a field, the notion of `rank of a matrix' as defined by `the dimension of subspace generated by columns of that matrix' is folklore and cannot be generalized to the class of matrices over an arbitrary commutative ring. The `determinantal rank' defined by the size of largest submatrix having nonzero determinant, which is same as the column rank of given matrix when the commutative ring under consideration is a field, was considered to be the best alternative for the `rank' in the class of matrices over a commutative ring. Even this determinantal rank and the McCoy rank are not so efficient in describing several characteristics of matrices like in the case of discussing solvability of linear system. In the present article, the `rank--function' associated with the matrix as defined in [{\it Solvability of linear equations and rank--function}, K. Manjunatha Prasad, \url{http://dx.doi.org/10.1080/00927879708825854}] is discussed and the same is used to provide a necessary and sufficient condition for the existence of an outer inverse with specific column space and row space. Also, a rank condition is presented for the existence of Drazin inverse, as a special case of an outer inverse, and an iterative procedure to verify the same in terms of sum of principal minors of the given square matrix over a commutative ring is discussed.

The rank of the average mixing matrix of trees with all eigenvalues distinct, is investigated. The rank of the average mixing matrix of a tree on n vertices with n distinct eigenvalues is bounded above by ⌈n/2⌉. Computations on trees up to 20 vertices suggest that the rank attains this upper bound most of the time. An infinite family of trees whose average mixing matrices have ranks which are bounded away from this upper bound, is given. A lower bound on the rank of the average mixing matrix of a tree, is also given.

This paper investigates conditions under which correlation matrices have a strictly positive dominant eigenvector. The sufficient conditions, from the Perron-Frobenius theorem, are that all the matrix entries are positive. The conditions for a correlation matrix with some negative entries to have a strictly positive dominant eigenvector are examined. The special structure of correlation matrices permits obtaining of detailed analytical results for low dimensional matrices. Some specific results for the $n$-by-$n$ case are also derived. This problem was motivated by an application in portfolio theory.

Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and in $Q$-norms, that extend and improve existing bounds.

In this paper, the nonlinear matrix equation $X^p+A^TXA=Q$, where $p$ is a positive integer, $A$ is an arbitrary $n\times n$ matrix, and $Q$ is a symmetric positive definite matrix, is considered. A fixed-point iteration with stepsize parameter for obtaining the symmetric positive definite solution of the matrix equation is proposed. The explicit expressions of the normwise, mixed and componentwise condition numbers are derived. Several numerical examples are presented to show the efficiency of the proposed iterative method with proper stepsize parameter and the sharpness of the three kinds of condition numbers.

The inclusion of students with mathematical learning disabilities (MLD) in the general education (GE) math classroom has become increasingly prevalent, and with the adoption of the Common Core State Standards, it has become the role of GE math teachers to ensure that all students work towards grade-level math standards. The following research utilized a survey to evaluate the perceptions of Wyoming middle-level math teachers in order to: (a) determine the extent of their knowledge and understanding of MLD and the disability dyscalculia; (b) examine the nature of their attitudes regarding MLD; (c) identify what supports and interventions are utilizing within their classroom to support learners with MLD; (d) explore what they see as the perceived barriers to providing instruction and/or supports to learners with MLD; and (e) examine whether teachers feel effective when working with students with MLD. An analysis of the data revealed that Wyoming middle-level math teachers believe they understand the impact of MLD and feel adequately prepared to teach students with MLD. However, qualitative data identified some perceived barriers related to working with students identified with MLD. The four biggest barriers overall were: (a) lack of training/knowledge about MLD; (b) lack of time to work with students in one-on-one instructional situations; (c) lack of resources (including special education personnel); and (d) pressure to have and meet the needs of all students in the GE math setting. The research also showed that perceived barriers play a part in whether teachers felt effective when working with students with MLD.

Writing in mathematics has been recommended by professionals and researchers for almost 30 years. The National Council of Teachers of Mathematics, Common Core State Standards, university professors, and employers have emphasized the need for individuals to write in mathematics. The purpose of this literature review is to explore and possibly make recommendations about using writing to help solve mathematics problems in middle school mathematics classes. This paper examines what the literature tells us about the use of writing in solving mathematics problems, what ways writing in mathematics can affect middle school comprehension, and how writing in mathematics can affect students’ metacognition. I also discuss how my findings in the literature apply to my classroom practice as a middle school mathematics teacher. Writing in mathematics has the potential to give the teacher valuable information, express students’ mathematical understandings, help students see mathematics as a process, and connect students’ mathematical ideas. In general, students tend to have greater mathematical ability in classrooms where mathematical writing is used. The effectiveness of writing in the middle school mathematics classroom depends on the classroom environment, scaffolding, frequency of student practice, and purpose of the writing assignment.

The human body utilizes various ions, including Copper, Zinc and Iron which are usually found attached to proteins, and free ions like Sodium, Potassium, Manganese, and Calcium. These ions are beneficial to the human body at trace amounts, but an increase in metal ions in the body have been recorded to have negative effects. An increase in Copper ions has been linked to Parkinson’s disease, Menkes disease, Wilson’s disease, Alzheimer’s disease and even cancer. Elevated Iron levels can be used by invading pathogens and also influence neurodegeneration (Wedd, A., & Maret, W., 2014). This illustrates the importance of researching the potential REDOX reactions between metal implants and bodily ions. Titanium alloys are widely used in medical applications due to a good mechanical strength and adequate corrosion resistance. However, Titanium tends to be a more expensive bio-metal. The application of Stainless steel alloys is substituted to decrease financial cost. These alloys maintain corrosion resistance by employing protective oxide surface layers (T.Hanawa, 2004). The purpose of this project is to evaluate REDOX reactions between ions in human bodily fluids and metals used in surgical implants. The effect of pH and temperature in Simulated Body Fluids (SBF) on the REDOX reaction rates will also be evaluated. The protective coating of oxide films, type of alloys, bio-corrosion and wear behavior of bio-metals has to be taken into consideration (Matusiewicz, Henryk, 2014). The results of this research could benefit further research into biocompatibility of implants in the human body.

In a mock project for Civil Engineering Senior Design Course, the infrastructure of Laramie, Wyoming is currently inadequate to accommodate future business opportunities and population growth. North Laramie is primarily a residential district with limited minor roads for residents to access Laramie business districts. This project focuses on a proposed minor arterial and development area to service the residential district in North Laramie and allow for future expansion. This alternate route will provide easy access points for truck traffic and business deliveries to North Laramie and the development area. The route will connect with Welsh Lane on the west near I-80, travel east across the Laramie River, connect with existing roads, continue east through the proposed development area and eventually turn south to connect with Grand Avenue at Vista Dr.

In the mock design project, the City of Laramie contracted Archimedes Engineering to design the minor arterial roadway. The scope of the project includes: a bridge and foundation design for crossing the Laramie River; traffic volume analyses; intersection and road alignment designs; pavement design; and hydrologic analyses of the development area for a detention pond and a drainage area for a storm water culvert design. The Archimedes Engineering team included seven members selected from the sub-disciplines of structural, water resources, transportation, and geotechnical engineering. Archimedes Engineering employed standard engineering practices to provide a safe, effective, and efficient route to service the future expansion of North Laramie.

Although the Contras exhibited appalling human rights violations while accepting hefty sums of money, weapons, logistical support, and U.S. man-power, much literature has succinctly removed any possibility for further analysis as to *who* the Contras were. It is the objective of this paper to break through this fairly inattentive, dwindling research and delve into the multifaceted, understudied topic of rural peasantry within the Contra conflict, 1979-90. When factoring that peasants constituted the bulk of foot-soldiers in the Contra ranks, their foundation was much more complex than initially understood. Underrepresented and reasonably voiceless in Nicaragua, rural peasants linked together in mass, joining the Contras out of government repression, a mandatory military draft, and agrarian reforms that challenged traditional ways of life. In one-on-one interviews with peasants, reasons for joining reflected familial and community propensities. Studying the peasantry also revealed subtle, overlooked variables in why the Contras were unable to provoke mass change in Nicaragua through a decade of strife. Through the use of interviews, economic data, polling, and newspaper articles, I offer an alternative explanation for the Contra’s failure. The Contra’s image was unable to unify a country filled with disconnectedness between urban and rural. In addition, few battles or saboteur acts ever crossed over into highly populated municipalities, leaving the majority of the population with limited, highly vetted information from the Nicaraguan government. By no means a comprehensive study, this paper attempts to draw a gap in the research for myself and others to re-activate historical discussion.

Mastitis is one of the leading reasons for culling ewes from U.S. flocks, and subclinical mastitis indicated by high somatic cell counts (SCC) in milk has also been shown to negatively impact ewe productivity. However, means to reduce subclinical mastitis and consequential effects on lamb production are sparse. A previous study which found deprived zinc levels in ewes with high SCC suggests that ewes supplemented with zinc may exhibit lower SCC and increased lamb performance (Murphy et al, 2018). In this study, yearling ewes (n = 59) were provided zinc above dietary recommendations during gestation and the effects on lamb performance measured by visual scores at birth and by weight gain. Ewes were divided into three treatment groups in which each ewe received one pound of a zinc sulfate fortified supplement containing 40 mg/kg zinc (control), 500 mg/kg, or 1000 mg/kg from approximately day 70 of gestation until parturition. Providing dietary zinc concentration during gestation did not affect lamb vigor scores, lamb weights, nor pounds of lamb weaned per ewe, but did increase lamb survival (P < 0.05). Pending serum zinc levels and somatic cell counts, along with data from two concurrent collaborative studies will provide further insight to the significance of this project.

Ethics is something which influences each of us on an everyday basis. Within this paper, I explore ethical philosophy and individual ethics within the judicial system. The knowledge is varied on a case by case basis but each respondent felt a greater degree of education in ethical philosophy would benefit our court system.

Drawing from qualitative research in the Ecuadorian Amazon, in this paper, we argue that Waorani indigenous people, and their everyday efforts at social reproduction, are sites through which an oil company and the state maintain and legitimize their governance of a complex territory defined at once as a national park, oil concession, and indigenous ancestral territory. Specifically, we show that corporate programs framed as improving living conditions in communities impacted by extraction, and Waorani culture and relationships to nature, are used as tools of resource governance by Repsol to the benefit of the state’s neo-extractivist project, enacted through social relations in this place. Despite the state’s increased role in sites of extraction as a result of its “post-neoliberal” (neo-) extractivist transition, Repsol continues its CSR programs; our focus on the embodied everyday experiences of resource governance in this place reveals that Repsol’s continued CSR-informed approach benefits the state’s neo-extractivist project even though it appears antithetical to “post-neoliberal” resource extraction. In this way, we contribute to the emerging literature on how neo-extractivism is managed and maintained on the ground, providing evidence for why this area of study deserves further research.

The travel and tourism industry is one of the world’s largest industries with a global economic contribution (direct, indirect, and induced) of over 7.6 trillion U.S. dollars in 2016. The direct economic impact of the industry in the areas of accommodation, transportation, entertainment, and attractions, was approximately 2.3 trillion U.S. dollars that year (United Nations World Tourism Organization, 2017). However, in recent years, the prevalence of terrorist attacks is causing hesitation in would-be travelers and stigmatizing certain destinations. According to *Statista*, the number of terrorist attacks in 2017 was 22,487, which includes acts of terrorism, insurgency, and politically- or ideologically-motivated violence by non-state actors--enough to cause widespread consequences within the tourism industry.

The goal of this project is to analyze the strategies and best practices of different marketing groups after terrorist acts have occurred. The scope will be on the psychological and financial reactions by both national and individual tourism companies after New York City 9/11, Paris 2015, the Nigerian Boko Haram kidnappings, and the Manchester and Las Vegas concert attacks. The results will likely suggest that proactive planning and comprehensive strategy will help people move past fear of terrorism and again encourage traveling to affected regions.

For the past five years, the University of Wyoming chapter of Engineers Without Borders (EWB-WYO) has worked with a small community in Guatemala to renovate the town’s water distribution system. Comunidad Maya receives its water supply from two spring box systems installed in nearby hills, but has suffered lately from insufficient water delivery. EWB-WYO has sent multiple teams to analyze the predicament from various angles and to ascertain the primary causes of the water shortage. These trips have been followed by periods of design and redesign, as EWB-WYO has sought the best long-term solution for the community.

In recent months, a design team of four students has created functional models of the entire pipe network, seeking to discover the regions of most critical loss within the system, and propose implementable changes. Various alternative designs were investigated and processed through multi-criteria decision and cost-benefit analyses. The most cost-effective, sustainable modifications were then selected for implementation, which is expected to take place in upcoming months.

The mining history of Bolivia and Mexico is tied to one of extractive industry, of the kind which made our modern world, and the complexity of its problems. In this context many of these raw materials are extracted to more advanced economies by large scale and intensely capitalist companies, these have immense power both in the economies of extraction but also everyday worker life. This relationship both at a micro and macro-level importantly shapes said countries labor relations and conditions, especially in respect to foreign managers and owners.

Specifically this project focuses on labor relations and complications in the long-standing standing history of exploitation of mining workforces, juxtaposed against a privileged class of often foreign managers and the economies this extraction bolstered. Based on this trajectory, I will argue that undoubtedly the Mining industries of Bolivia and Mexico have represented extraction capitalism, arguably the system which has created our world, at its worst with a long a defining history tied to their positioning on the world stage. This is reflected badgering pseudo-control of States through powerful multi-national corporations and deplorable conditions for miners, but they also became an important battleground, sometimes literally, for great and sweeping labor and political change as reflected in the Mexican Revolution of the 1900-1910s and the Bolivian Revolution of 1952. These successes in turn however often lead to further failures, and the labor history of extractive mining in Mexico and especially Bolivia, has been defined by cycles and little real conditional change, even in contemporary times.

In order to provide insight into the effectiveness of messages about racial equality for black Americans, this project utilized Critical Race Theory (CRT) to assess and juxtapose two Malcolm X speeches with rhetoric from the Black Lives Matter (BLM) movement, through neo-Aristotelian Criticism. The messages from Malcolm X’s two speeches and the rhetoric from the BLM movement were extrapolated and defined through Critical Race Theory. Themes of globalization, Black Nationalism, epistemology, white-centricity, black-affirmation, self-identification, imagery, and media bias have been touched on and explored. The speeches, the rhetoric and all of their elements were placed in their historical contexts. In accordance with neo-Aristotelian Criticism, the messages of the Malcolm X speeches and the BLM rhetoric were evaluated using the five canons of rhetoric. Finally, the messages of the speeches and the rhetoric were analyzed for effectiveness given their historical context and their use of the five canons of rhetoric.

This study investigates the perceptions and attitudes that bilinguals hold towards Spanish-English code-switching in Wyoming. ¨Code-switching is the alternation of two languages in a single discourse, sentence or constituent¨ (Poplack, 1980). Many studies including, Hidalgo (1988), Toribio (2002), Parama, Kreiner, Stark, Schuetz (2017), and others have researched the sociolinguistic attitudes towards code-switching. This study will focus on sociolinguistic attitudes as well, by looking at the general sentiment towards code-switching between English and Spanish in a rural area. It is hypothesized that subjects will hold a similar attitude towards code-switching as shown in the studies mentioned, a dislike of the sound and use of switching between languages in a single turn of speaking. Attitudes and perceptions are evaluated by a questionnaire that each subject fills out. Their attitudes are rated on a five point Likert scale. The purpose is to discover if a less populated place with a smaller Hispanic population, like Wyoming, will show negative attitudes or will rather align with a more favorable view, despite a low amount of linguistic contact (Escobar y Potowski, 2015) and Hispanic population. Results will also show how the sentiments have extended or have changed from 1988 to 2018 based on findings from Hidalgo (1988). Results showed a generally positive attitude in Wyoming that contradicts with previous studies.